Inventiones mathematicae

, Volume 163, Issue 1, pp 1–24

Correlations for pairs of closed geodesics

  • Mark Pollicott
  • Richard Sharp
Article

DOI: 10.1007/s00222-004-0427-7

Cite this article as:
Pollicott, M. & Sharp, R. Invent. math. (2006) 163: 1. doi:10.1007/s00222-004-0427-7

Abstract

In this article we consider natural counting problems for closed geodesics on negatively curved surfaces. We present asymptotic estimates for pairs of closed geodesics, the differences of whose lengths lie in a prescribed family of shrinking intervals. Related pair correlation problems have been studied in both Quantum Chaos and number theory.

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • Mark Pollicott
    • 1
  • Richard Sharp
    • 2
  1. 1.Department of MathematicsWarwick UniversityCoventryUK
  2. 2.Department of MathematicsUniversity of ManchesterManchesterUK